In many cases high-frequency components are being characterized with a sine wave signal. Due to the non-linear behaviour of components the resulting signals contain harmonics.
To test components in more realistic circumstances, often a modulated sine wave is applied. Due to the non-linear behaviour of the component under test, the resulting signal now contains modulated harmonics. The modulation bandwidth increases due to the non-linear behaviour and increases with the number of harmonics. Also around DC, the modulation can manifest itself (FIG. 1).
When testing mixers under modulation conditions, one can expect harmonics of the local oscillator (LO) frequency and of the main modulated input frequency and mixing products of both to be present at all mixer ports. As such one can identify different discrete tones in the frequency domain at the mixing products of the LO frequency fLO and the main input frequency f1, also called the carrier. These tones are being modulated and possibly broadened depending on the mixing products (FIG. 2a).
The analogue signals x(t) under consideration comprise a set of discrete tones (including DC) which are modulated. The modulation possibly can come from different sources and may be phase coherent or phase incoherent. The modulation signals themselves can have a discrete or continuous spectrum as illustrated in FIG. 2b. 
This type of signal x(t) is measured with one or another type of receiver, converting the analogue signal into a set of numbers xRec(k) that represent the input signal (FIG. 3). These numbers can be in time-domain or frequency-domain or a combination thereof. The representation domain is not of any importance.
The receiver measuring the above type of signals is kept in its linear region of operation by limiting the signal peak amplitude, thus avoiding the introduction of any non-linear effect on the measured signal. Nevertheless, the receiver distorts the signal in amplitude and phase as function of the frequency through its inherent linear filtering characteristics. Due to this linear filtering effect represented by a transfer function, it is not possible to reconstruct the original signal x(t) directly from the numbers xRec(k) in the representation domain.
To reconstruct/measure the high frequency signal x(t) correctly, it is necessary to determine the receiver transfer characteristic in amplitude and phase as a function of frequency. To determine the transfer function, one applies a well known input signal x(t), resulting into a series of numbers XRec(k) from which the distorting transfer function can be calculated accurately. This signal, which is called “reference” or “calibration” signal, is further assumed to be perfectly known.
To measure/reconstruct a signal being distorted by the receiver, the transfer function must be determined at the frequencies or frequency bands related to the measured signal. As such also the “reference” signal must have power at the frequencies and/or in the frequency bands where one needs to know the transfer function. To determine the transfer characteristic accurately, in many cases a frequency-selective measurement is performed to determine amplitude and phase distortion at discrete frequency tones. Therefore, the “reference” signal is created so that it contains discrete tones by making sure that the “reference” signal is a periodic signal.
There is a need for an efficient hardware implementation to create a reference signal with discrete tones, optimized for the type of signals of FIG. 2b such that power is present at frequencies and frequency bands of interest.
To determine the transfer function in amplitude, well-known power calibration techniques exist. To determine the transfer function in phase, one technique is to apply a signal known in phase (calibration or reference signal) at the receiver input and to compare the measured response with the known signal. Possibly the interaction of the receiver with the device generating the calibration signal needs to be characterized and corrected for. Different means, like a network analyzer set-up, can be used for this purpose by measuring the reflection factor of the device generating the reference signal and by assuming a flow graph as equivalent model. This type of correction is well known in the art.
Further also techniques exist to know the phase content of the calibration or reference signal. This signal is typically a narrow pulse with a broad frequency content. Knowing the signal not only in phase but also in power allows determining at the same time the amplitude and phase of the receiver transfer function.
Only real-time receivers have the possibility to measure a one-shot broadband calibration signal and even with this type of receivers it is better to apply a periodic signal to improve signal-to-noise ratio by measuring longer traces, equal to a multiple of periods. To determine the transfer function using one or another form of a well known periodic signal, the calibration or reference signal must have power at least at the frequencies of interest.
Nowadays this is typically done by creating a dense enough frequency grid by using a narrow pulse, which can be characterized accurately and which is fired with a low periodicity. The pulse width in combination with the pulse shape determines the highest available frequency components and the periodicity of firing determines the frequency grid density (FIG. 4). To create a dense grid, the fundamental frequency of the harmonics must below. A fundamental problem with this approach is that the power spectrum is very low in power because the peak amplitude of the pulse must be limited in order not to overdrive the receiver to avoid any non-linear distortion on the signal to be measured. As such a large dynamic range is required for the receiver just to perform the calibration. This can be understood easily. Suppose one wants to measure a RF signal with 1 GHz carrier, three harmonics and modulated with a signal of 10 kHz periodicity. This results in discrete tones of k×1 GHz+I×10 kHz, which is a sparse frequency grid. With the approach illustrated in FIG. 4, one runs a pulse generator at the low frequency rate of 10 kHz to create a dense grid of tones to cover the required frequency grid. To cover the highest required harmonic of 3 GHz, the pulse needs to be very short compared to the repetition rate. Therefore, there is only power present during a very short time compared to the repetition rate of 0.1 ms. As a result the power spectrum is very low because the power spreads across all the spectrum components with a spacing of 10 kHz at least up to 3 GHz (300 000 spectral components).
It is known that by using a Pseudo-Random Binary Sequence (PRBS) sequence it is possible to increase the power spectrum (FIG. 5). However, for both cases the frequency grid density is equally spaced from DC to the highest frequency components, which in most cases covers many more frequencies than required by the measurement signals. The power spectrum is higher because the pulses are fired at a higher frequency and the periodicity is realized by dropping out pulses in a specific sequence, determined by the PRBS sequence.
Certain receivers are narrowband and cannot measure the signals as illustrated in FIG. 3 at once. They need to scan the measured signal frequency band by frequency band and need to reconstruct the original analogue signal after the conversion to numbers. Jumping from frequency band to frequency band the phase coherence is lost for most receiver topologies. To establish phase coherence though, an additional separate receiver, coherently measuring in parallel with the measurement receiver, measures a signal having the same properties as the above-mentioned calibration or reference signal. This calibration or reference signal has phase coherence by construction. The difference is that for this signal one does not need to know the phase values of the spectral components. The only requirement is that the signal be stable so that the measured signal can be normalized against it. This signal is referred to as a “synchronization signal”. As such the “synchronization signal” is the same as the “calibration or reference signals” except that one does not need to know its phase values neither the amplitude values.
In the prior art solutions as explained above, the power of the “reference” or the “synchronization” signal is smeared over the full frequency range of the signal with a spectral density equal to the periodicity of the signal. As such the power spectral density function is very low and requires a high dynamic range of the receiver already only for calibration or synchronization purposes. Hence, there is a need for a solution where the frequency tones (and as such the available power of the signal) are concentrated around a discrete list of tones, typically the fundamental frequency and some of its harmonics, or even are concentrated on an arbitrary given set of frequencies, depending on the signals to characterize. This solution can be used to determine the phase characteristic of a receiver with a lower dynamic range at the frequencies of interest. The frequencies of interest are enforced by the type of signals to measure. Also this solution can be used to synchronize the receiver with a synchronization signal at a lower dynamic range while moving from one frequency to another.